Cut cauliflower into pieces and microwave with a small amount of water for 8 minutes on high, or until soft. Drain, then mash or puree cooked cauliflower.
Melt butter in a saucepan over medium heat then add flour and stir until smooth. Cook for 1-2 minutes.
Add 1/2 cup of milk and stir or whisk until incorporated. Continue adding milk in 1/2 cup increments, whisking until smooth each time. Stir until sauce thickens and then add grated cheese and cauliflower.
Heat the oil in a frypan over high heat. Add onion and garlic and cook, stirring continuously, until soft.
Add mince and cook until browned, then add jar of pasta sauce and reduce to a simmer. Cook for about 15 minutes until sauce has thickened but is not too dry.
Spread half the meat sauce in the bottom of your dish, followed by a layer of lasagne sheets (cut to size as required) and half the white sauce. Repeat. Top with extra grated cheese.
Bake at 180C for about 30 minutes until cheese is melted.